Animals tend to reinvade areas that they have been exterminated from,
if surrounding populations are healthy. If you manipulate habitats
to make them unsuitable for a species, these unsuitable habitats will not
be reinvaded, even when surrounding populations are healthy. For
this reason, exclusion or habitat modification always works better in the
long run than does local extermination.

Pigeons roost and nest in cubby holes, under bridges and in the eaves
and ledges of buildings.

Pigeons are capable of traveling long distances on a daily basis for
food or water.

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